2
lesson pretestMultiple Choice

Pretest

Question 2 • Mathematics II

Consider cap u is equal to x divides x is A negative real number Which is an empty set?

Answer
A
start set x such that x is in cap u and x has A negative square root end set
B
start set x such that x is in cap u and x is equal to the sum of one negative and one positive number end set
C
start set x such that x is in cap u and x has A negative cube root end set
D
start set x such that x is in cap u and x is equal to the product of A positive number and minus 1 end set

Explanation

The universal set contains only negative real numbers. A real number with a square root must be nonnegative, since squaring any real number gives a nonnegative result. So no negative real number has a real square root, making choice A, “x has a negative square root,” an empty set. The other conditions can each be satisfied by negative real numbers.

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